The need for judgement in geotechnical reliability studies

ABSTRACT

A core principle of geotechnical engineering practice is the need to exercise judgement in evaluating soil and site conditions and in performing analyses. The requirement for considering judgement applies equally to performing deterministic or probabilistic analyses. In addition, for probabilistic analyses, choices must be made among the possible methods of analysis and the method of characterising variables. Consequently, geotechnical reliability studies inevitably involve significant uncertainties, and judgement is needed to perform reliability analyses and to evaluate the results. Two case histories, briefly described here, show that judgement and experience are essential prerequisites for meaningful assessment of geotechnical reliability.     

Response surface-based robust geotechnical design of supported excavation – spreadsheet-based solution

ABSTRACT

The robust geotechnical design (RGD) approach which involves optimization to obtain a design that is safe, cost-efficient, and robust in the face of uncertainties, can be computationally challenging for complex geotechnical structures. In this study, the RGD approach has become practical by introducing a response surface as a surrogate to finite element- or finite difference-based computer code that is used for analyzing the system, and developing a fast algorithm for the optimization process. For demonstration purposes, a real-world supported excavation project is designed using this modified RGD approach and it is compared with the one designed by a local expert.     

Offshore pile system model biases and reliability

ABSTRACT

Recent hurricanes between 2004 and 2008 in the Gulf of Mexico provide valuable new information about design model biases and uncertainties because multiple offshore platforms were loaded beyond the predicted capacity of their pile systems and because there was a failure of a pile system. A Bayesian calibration of model bias factors based on predicted versus observed performance of pile systems in hurricanes indicates that the conventional American Petroleum Institute design method for pile capacity is slightly conservative by about 10% for base shear (i.e. lateral) failures of pile systems in clay, unbiased for overturning (i.e. axial) failures of pile systems in clay, and conservative by more than 50% for overturning failures of piles systems in sand. The epistemic uncertainty in the updated bias factors is represented by coefficient of variation values of about 0.25 for base shear and overturning failures of pile systems in clay and 0.35 for overturning failures of pile systems in sand. A reliability assessment with the calibrated model bias factors shows that the current design practice produces lower reliability for a pile system with three piles versus one with eight piles and lower reliability for a pile system failing in overturning versus one failing in base shear. Therefore, the current design practice could potentially be improved by taking into account the mode of failure and the redundancy in the pile system to provide for a more uniform level of reliability.     

A Methodology for Reliability-Based Design of Rock Slopes

Summary A reliability-based methodology for the design of rock slopes, that can easily be implemented by the practicing engineers is proposed. The advanced first-order second-moment (AFOSM) method is adopted as the reliability assessment model and its application is illustrated for the case of plane failure. A model is developed within the framework of first-order second-moment approach to analyze the uncertainties underlying the in situ shear strength properties of rock discontinuities. Here, particular emphasis is given on the assessment of uncertainties related to the shear characteristics of clean, unfilled rock discontinuities under low normal stress levels. An extensive literature survey on the shear characteristics of discontinuities is carried out in order to collect data for the quantification of uncertainties. The data extracted from this literature survey are classified and reprocessed so that they can be utilized in the uncertainty analysis model. A user friendly software called ROCKREL is developed to carry out the numerical computations and to make the proposed design format more practical. Received April 16, 2001; accepted June 10, 2002; Published online November 19, 2002 Authors' address: Prof. Celal Karpuz, Middle East Technical University, Faculty of Engineering, Department of Mining Engineering, 06531 Ankara, Turkey; e-mail: karpuz @metu.edu.tr     

Reliability analysis of the bearing failure problem considering uncertain stochastic parameters

The consideration of uncertainties plays an increasing role in the design of geotechnical structures. An important procedure in the uncertainty analysis is the reliability assessment whereby the required statistical quantities and distributions are assumed to be known exactly. Due to small sample observations and missing information this is not the case in practical applications and uncertainties in the stochastic parameters themselves have to be considered. In our study we estimate the parameter variation of soil properties by statistical procedures and perform an extended reliability analysis of a shallow foundation considering these uncertainties. We propose a novel approach based on a Taylor series expansion which enables the estimation of the failure probability variation very efficiently.     

Reliability analysis of shallow foundations in reference to design codes development

In this study, FORM analysis is carried out for shallow foundation of a typical building in order to evaluate relative magnitude of uncertainties involved in the force and the resistance sides. The distinguished feature of this study is to take into account the uncertainty of the earthquake force as much as possible. Tthis is because, the seismic design dominates major part of structural design in Japan, and without referring to this problem, no useful information of practical value is gained. The results of the FORM analysis exhibited the reliability index values between 2.0 to 3.5, which is considered to be in a reasonable range. Since the 50 year maximum earthquake force is considered in the reliability calculation, calculated reliability index values are for the period of 50 years. The sensitivity factor obtained in a case more realistic ground variability is taken into account exhibited values not very different from those obtained in the upper structures.     

Effect of site-specific soil nonlinearities and uncertainties on ground motion intensity measures and structural demand parameters

ABSTRACT

This paper investigates the effects of site-specific uncertainties in soil strength and stiffness parameters on the commonly used ground motion intensity measures and the resulting engineering demand parameters of moment resisting frames of varying heights at a site in Los Angeles, California. Through a detailed site-specific uncertainty analysis, comparison with generic data, and an extensive parametric study, it is shown that underestimation or overestimation of the true soil uncertainties could significantly affect both the average values and variabilities of the Arias intensity and PGA, and that the uncertainty in the soil strength parameter has more profound effect on the intensity measures than the uncertainty in the soil stiffness parameter. It is also shown that depending upon the natural period of a structure, the uncertainty in both the soil strength and stiffness parameters could affect its peak floor acceleration and peak inter-story drift. Moreover, it is observed that the structure amplifies the soil uncertainty more than the seismological uncertainty.     

MCS-based probabilistic design of embedded sheet pile walls

A probabilistic approach to the design of embedded sheet pile walls is developed in this paper. The approach is based on Monte Carlo simulation (MCS), and it is used to investigate the performance of the partial factors and different design approaches in Eurocode 7 in achieving the target degrees of reliability. The approach is illustrated through an embedded sheet pile wall design example that has been used in literature for the evaluation of Eurocode 7. The approach deals rationally with the correlated load and resistance, and it bypasses a difficult but frequently asked question in Eurocode 7 (i.e. should the passive earth pressure be considered as a load (i.e. action) or a resistance?). The probabilistic design approach (DA) is also used to explore the effects of the soil unit weight variability and uncertainties in over-digging depth and wall friction. The effects of uncertainties in over-digging depth and wall friction are found to be significant. It is also found that, although the soil unit weight variability is generally minor, its effect on the design of embedded sheet pile walls is significant and should be properly accounted for in the design. The MCS-based probabilistic DA proposed in this study provides a straightforward way for proper consideration of such variability with relative ease.     

Development of partial factor design method on bending strength of piles for Japanese Specifications for Highway Bridges

ABSTRACT

This paper describes the development of a partial factor design method on the bending strength of piles for the Japanese Specifications for Highway Bridges. First, uncertainties in mobilised bending moments and yield bending moments were evaluated by Monte Carlo simulations. Second, the reliability of piles designed by the previous specifications were evaluated on the basis of reliability analysis considering uncertainties in the mobilised bending moments, yield bending moments, and other factors. Finally, a partial factor design method utilising a survey subsurface investigation method and ground type was developed to reach target reliability levels determined by the Standards.     

Categorisation and Harmonisation of Probabilistic Earthquake Hazard Assessments with Respect to Statistic Representation of Input Data

Probabilistic hazard calculations were tested with respect to input data uncertainties. Statistical approximations of input data allow the regression coefficients and their standard deviations to be determined. Since inaccuracies of the regressions closely depend on the input data uncertainties, the standard deviations of the individual coefficients were used as a measure of input data parametrisation. Differences in the hazard outputs, caused only by various combinations of the regression coefficients and their standard deviations determined for the cumulative recurrence graph and the attenuation law, were studied. It was concluded that the hazard calculation conditions should be (a) strictly defined and always quoted with every hazard assessment, and (b) standardized in order to establish a common liability of earthquake hazard calculations. The established categorisation of the earthquake hazard assessments divides the probabilistic hazard calculations according to their reliability and helps users to apply them in earthquake engineering practice. The credible hazard assessments corresponding to 90% probability can be recommended for common structures whereas the maximum credible hazard assessments coinciding with 95% probability yield values close to hazard assessments of important structures, hospitals, bridges, etc.     

Structural stability of gravity dams: a progressive assessment considering uncertainties in shear strength parameters

Structural sliding stability of gravity dams is generally quantified using deterministic factor of safety, FS_det. Large FS_det (e.g. 3 in normal condition), are used in existing guidelines to guard against material and load uncertainties. Some guidelines allow an arbitrary reduction in FS_det (e.g. 2) when the knowledge in strength parameters increases from material test data. Yet, those reduced FS_det are not based on a rational consideration of uncertainties. Propagation of uncertainties could be done using probabilistic analyses, such as Monte-Carlo simulations (MC) which are complex and challenging for practical use. There is thus a need to develop simplified reliability based safety assessment procedures that could rationalise the adjustment of FS_det. This paper presents a progressive analysis methodology using four safety evaluation formats of increasing complexity: (i) deterministic, (ii) semi-probabilistic (partial coefficient), (iii) reliability based Adjustable Factor of Safety (AFS), and (iv) probabilistic. Comprehensive comparisons are made for the sliding safety evaluation of a 80 m gravity dam. Results are presented in terms of sliding factors of safety, allowable water levels, and demand/capacity ratios. It is shown that the AFS formulation, using direct integration, is simple and practical to use in complement to existing dam safety guidelines before undertaking MC simulations.     

Construction of variance-based metamodels for probabilistic seismic analysis and fragility assessment

Finite element models used in industrial studies for seismic structural reliability analysis are in general very complex and computationally intensive. This is due to the important number of degrees of freedom as well as due to advanced damage models and failure modes that have to be simulated. In consequence, reliability studies are feasible only by means of simpler surrogate models able to represent essential physics. Then the choice of an accurate surrogate or metamodel is crucial for uncertainty propagation and sensitivity analysis. The construction of a pertinent metamodel is however a not simple task when random uncertainties, not explained by the model parameters, have to be accounted for. This is the case for transient seismic analysis where the ground motion, an intrinsically random phenomena, is modelled by a stochastic process that cannot be entirely described by a set of parameters. In this paper, we construct a versatile metamodel based on analysis of variance (ANOVA) decomposition. The ANOVA decomposition provides a convenient framework allowing both for parametric uncertainties and for stochastic variability introduced by seismic load. We then compute fragility curves and perform sensitivity analysis.     

Probabilistic comparative analysis between design rules of a shallow foundation safety

ABSTRACT

A fact that is generally overlooked in many geotechnical uncertainty analyses is that input data of the model may be correlated. While this correlation may influence the system response, epistemic uncertainties i.e. lack of knowledge of this correlation appears as a risk factor. This paper discusses how a negative correlation between cohesion (c’) and friction angle (Ø’) with their associated uncertainties can influence both the bearing resistance of a shallow strip foundation footing and the estimation of its safety. A probabilistic approach that considers both the negative correlation and the uncertainty is used in this work as a reference. This method is compared to Eurocode 7 variants that do not for the correlation. These variants, resistance and material factoring methods appears to be more or less conservative depending on the negative correlation degree between (c’–Ø), their associated uncertainties and soil configurations. Finally, the proposed probabilistic comparison shows that the material factoring method is more conservative than the resistance one.     

Development of partial factor design method on bearing capacity of pile foundations for Japanese Specifications for Highway Bridges

ABSTRACT

This paper shows the development of a partial factor design method on the bearing capacity of pile foundations for Japanese Specifications for Highway Bridges. Firstly, estimation design equations on the bearing capacities of pile foundations are improved by analysis of pile load test results and uncertainties in the bearing capacities are evaluated. Secondly, the reliabilities of pile foundations designed by the former specifications are evaluated based on reliability analysis considering the uncertainties in the bearing capacities and coefficients of subgrade reaction. Finally, a partial factor design method is developed based on the target reliability index obtained based on the conventional pile installation method by the pile installation methods. The factors are different for each pile installation method.     

基于Copula函数的CFG桩复合地基载荷-变形曲线的概率分析

CFG桩(cement-fly ash-gravel pile)复合地基是一种重要的地基处理形式,在日益增加的大面积住宅和商业开发中作用越来越突出,然而该种桩型的加卸荷-沉降变形特性仍然需深入研究,尤其在概率评估方面。根据北京星光影视股份有限公司生产科研基地项目工地中的21根CFG桩单桩静载试验和32个复合地基静载试验的原位加卸载测试成果,采用两参数的双曲线或幂曲线回归拟合了每一条加荷-变形曲线。由于土体的内在各向异性和其强度的变异性,评估整个场地的加荷-变形曲线时,其回归参数表现出了较大的离散性。将一个场地的多组回归参数组成一个随机向量,其加载-位移曲线的不确定性可由简单的两变量随机向量体现,引入双变量联结函数（Copula）描述随机回归参数间的相依性。最后,考虑正常使用极限状态,采用基于Copula函数的模拟模型计算了CFG桩复合地基的可靠度指标。研究结果有助于改进CFG桩复合地基的概率设计与评估。     

An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O–Na2O–CaO–MgO–MnO–FeO–Fe2O3–Al2O3–TiO2–SiO2–C–H2–O2

We present, as a progress report, a revised and much enlarged version of the thermodynamic dataset given earlier (Holland & Powell, 1985). This new set includes data for 123 mineral and fluid end-members made consistent with over 200 P–T–X_CO2–f_O2 phase equilibrium experiments. Several improvements and advances have been made, in addition to the increased coverage of mineral phases: the data are now presented in three groups ranked according to reliability; a large number of iron-bearing phases has been included through experimental and, in some cases, natural Fe:Mg partitioning data; H₂O and CO₂ contents of cordierites are accounted for with the solution model of Kurepin (1985); simple Landau theory is used to model lambda anomalies in heat capacity and the Al/Si order–disorder behaviour in some silicates, and Tschermak-substituted end-members have been derived for iron and magnesium end-members of chlorite, talc, muscovite, biotite, pyroxene and amphibole. For the subset of data which overlap those of Berman (1988), it is encouraging to find both (1) very substantial agreement between the two sets of thermodynamic data and (2) that the two sets reproduce the phase equilibrium experimental brackets to a very similar degree of accuracy. The main differences in the two datasets involve size (123 as compared to 67 end-members), the methods used in data reduction (least squares as compared to linear programming), and the provision for estimation of uncertainties with this dataset. For calculations on mineral assemblages in rocks, we aim to maximize the information available from the dataset, by combining the equilibria from all the reactions which can be written between the end-members in the minerals. For phase diagram calculations, we calculate the compositions of complex solid solutions (together with P and T) involved in invariant, univariant and divariant assemblages. Moreover we strongly believe in attempting to assess the probable uncertainties in calculated equilibria and hence provide a framework for performing simple error propagation in all calculations in thermocalc, the computer program we offer for an effective use of the dataset and the calculation methods we advocate.     

浅论岩土工程极限状态设计基本思想

论述了岩土工程极限状态设计的基本思想,包括极限状态的概念、土工参数设计值的确定过程和方法、构造物的重要度和场地地基复杂程度的划分、岩土工程类别、作用载荷组合、分项安全系数和极限状态设计等;给出了土工参数的实测值、导出值、标准值和设计值的确定原则或方法;指出在极限状态设计中,可通过增大设计作用效应或降低设计抗力的方法来进行岩土工程的可靠性设计.     

Defining and selecting characteristic values of geotechnical parameters for designs to Eurocode 7

ABSTRACT

Recent geotechnical design codes (such as Eurocode 7) aim to achieve geotechnical designs with an appropriate target reliability by applying partial factors to characteristic parameter values. Development in Eurocode 7 of the definition and selection of the characteristic values is traced. A significant development occurred with the definition of the characteristic value as a cautious estimate of the value affecting the occurrence of the limit state. Statistical equations to select characteristic values are presented, including one proposed for the revised of Eurocode 7.An alternative equation reduces the amount of subjective judgement and is more likely to achieve the target reliability.     

考虑计算参数不确定性的边坡稳定分析

岩土体当中存在大量的不确定因素,给边坡的稳定性分析判断带来了困难。在分析了计算参数的不确定性是影响分析可靠性的主要原因的基础上,运用模糊集理论考虑计算参数的不确定性,提出了模糊参数的具体构造方法和边坡稳定的不确定性分析思路。该方法可以根据不同隶属度下的参数截集区间,计算出相应隶属度下的安全系数区间,并可由此得到边坡的可靠性指标和安全系数建议值。通过不同算例研究表明,使用此方法能充分考虑计算参数的不确定性,得到的安全系数更加科学可靠。     

The geological and geotechnical design model in tunnel design: estimation of its reliability through the R-Index

ABSTRACT

In this paper recent improvements of the R-Index method are presented, based on its application on several projects in various geological and geotechnical contexts. The R-Index derives from a probabilistic procedure conceived for estimating the reliability level of the Geological and Geotechnical Design Model used to design underground structures, especially tunnels. The R-Index takes into account the geological complexity of a site and recommended empirical scores (based on expert judgement) for different quality levels of geological surveys and geotechnical and geophysical investigations.